sbv-8.11: Data/SBV/Tools/Overflow.hs
-----------------------------------------------------------------------------
-- |
-- Module : Data.SBV.Tools.Overflow
-- Copyright : (c) Levent Erkok
-- License : BSD3
-- Maintainer: erkokl@gmail.com
-- Stability : experimental
--
-- Implementation of overflow detection functions.
-- Based on: <http://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/z3prefix.pdf>
-----------------------------------------------------------------------------
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE ImplicitParams #-}
{-# LANGUAGE Rank2Types #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeApplications #-}
{-# LANGUAGE UndecidableInstances #-}
{-# OPTIONS_GHC -Wall -Werror #-}
module Data.SBV.Tools.Overflow (
-- * Arithmetic overflows
ArithOverflow(..), CheckedArithmetic(..)
-- * Cast overflows
, sFromIntegralO, sFromIntegralChecked
) where
import Data.SBV.Core.Data
import Data.SBV.Core.Kind
import Data.SBV.Core.Symbolic
import Data.SBV.Core.Model
import Data.SBV.Core.Operations
import Data.SBV.Core.Sized
import GHC.TypeLits
import GHC.Stack
import Data.Int
import Data.Word
import Data.Proxy
-- Doctest only
-- $setup
-- >>> import Data.SBV.Provers.Prover (prove, allSat)
-- | Detecting underflow/overflow conditions. For each function,
-- the first result is the condition under which the computation
-- underflows, and the second is the condition under which it
-- overflows.
class ArithOverflow a where
-- | Bit-vector addition. Unsigned addition can only overflow. Signed addition can underflow and overflow.
--
-- A tell tale sign of unsigned addition overflow is when the sum is less than minimum of the arguments.
--
-- >>> prove $ \x y -> snd (bvAddO x (y::SWord16)) .<=> x + y .< x `smin` y
-- Q.E.D.
bvAddO :: a -> a -> (SBool, SBool)
-- | Bit-vector subtraction. Unsigned subtraction can only underflow. Signed subtraction can underflow and overflow.
bvSubO :: a -> a -> (SBool, SBool)
-- | Bit-vector multiplication. Unsigned multiplication can only overflow. Signed multiplication can underflow and overflow.
bvMulO :: a -> a -> (SBool, SBool)
-- | Same as 'bvMulO', except instead of doing the computation internally, it simply sends it off to z3 as a primitive.
-- Obviously, only use if you have the z3 backend! Note that z3 provides this operation only when no logic is set,
-- so make sure to call @setLogic Logic_NONE@ in your program!
bvMulOFast :: a -> a -> (SBool, SBool)
-- | Bit-vector division. Unsigned division neither underflows nor overflows. Signed division can only overflow. In fact, for each
-- signed bitvector type, there's precisely one pair that overflows, when @x@ is @minBound@ and @y@ is @-1@:
--
-- >>> allSat $ \x y -> snd (x `bvDivO` (y::SInt8))
-- Solution #1:
-- s0 = -128 :: Int8
-- s1 = -1 :: Int8
-- This is the only solution.
bvDivO :: a -> a -> (SBool, SBool)
-- | Bit-vector negation. Unsigned negation neither underflows nor overflows. Signed negation can only overflow, when the argument is
-- @minBound@:
--
-- >>> prove $ \x -> x .== minBound .<=> snd (bvNegO (x::SInt16))
-- Q.E.D.
bvNegO :: a -> (SBool, SBool)
instance ArithOverflow SWord8 where {bvAddO = l2 bvAddO; bvSubO = l2 bvSubO; bvMulO = l2 bvMulO; bvMulOFast = l2 bvMulOFast; bvDivO = l2 bvDivO; bvNegO = l1 bvNegO}
instance ArithOverflow SWord16 where {bvAddO = l2 bvAddO; bvSubO = l2 bvSubO; bvMulO = l2 bvMulO; bvMulOFast = l2 bvMulOFast; bvDivO = l2 bvDivO; bvNegO = l1 bvNegO}
instance ArithOverflow SWord32 where {bvAddO = l2 bvAddO; bvSubO = l2 bvSubO; bvMulO = l2 bvMulO; bvMulOFast = l2 bvMulOFast; bvDivO = l2 bvDivO; bvNegO = l1 bvNegO}
instance ArithOverflow SWord64 where {bvAddO = l2 bvAddO; bvSubO = l2 bvSubO; bvMulO = l2 bvMulO; bvMulOFast = l2 bvMulOFast; bvDivO = l2 bvDivO; bvNegO = l1 bvNegO}
instance ArithOverflow SInt8 where {bvAddO = l2 bvAddO; bvSubO = l2 bvSubO; bvMulO = l2 bvMulO; bvMulOFast = l2 bvMulOFast; bvDivO = l2 bvDivO; bvNegO = l1 bvNegO}
instance ArithOverflow SInt16 where {bvAddO = l2 bvAddO; bvSubO = l2 bvSubO; bvMulO = l2 bvMulO; bvMulOFast = l2 bvMulOFast; bvDivO = l2 bvDivO; bvNegO = l1 bvNegO}
instance ArithOverflow SInt32 where {bvAddO = l2 bvAddO; bvSubO = l2 bvSubO; bvMulO = l2 bvMulO; bvMulOFast = l2 bvMulOFast; bvDivO = l2 bvDivO; bvNegO = l1 bvNegO}
instance ArithOverflow SInt64 where {bvAddO = l2 bvAddO; bvSubO = l2 bvSubO; bvMulO = l2 bvMulO; bvMulOFast = l2 bvMulOFast; bvDivO = l2 bvDivO; bvNegO = l1 bvNegO}
instance (KnownNat n, BVIsNonZero n) => ArithOverflow (SWord n) where {bvAddO = l2 bvAddO; bvSubO = l2 bvSubO; bvMulO = l2 bvMulO; bvMulOFast = l2 bvMulOFast; bvDivO = l2 bvDivO; bvNegO = l1 bvNegO}
instance (KnownNat n, BVIsNonZero n) => ArithOverflow (SInt n) where {bvAddO = l2 bvAddO; bvSubO = l2 bvSubO; bvMulO = l2 bvMulO; bvMulOFast = l2 bvMulOFast; bvDivO = l2 bvDivO; bvNegO = l1 bvNegO}
instance ArithOverflow SVal where
bvAddO = signPick2 bvuaddo bvsaddo
bvSubO = signPick2 bvusubo bvssubo
bvMulO = signPick2 bvumulo bvsmulo
bvMulOFast = signPick2 bvumuloFast bvsmuloFast
bvDivO = signPick2 bvudivo bvsdivo
bvNegO = signPick1 bvunego bvsnego
-- | A class of checked-arithmetic operations. These follow the usual arithmetic,
-- except make calls to 'Data.SBV.sAssert' to ensure no overflow/underflow can occur.
-- Use them in conjunction with 'Data.SBV.safe' to ensure no overflow can happen.
class (ArithOverflow (SBV a), Num a, SymVal a) => CheckedArithmetic a where
(+!) :: (?loc :: CallStack) => SBV a -> SBV a -> SBV a
(-!) :: (?loc :: CallStack) => SBV a -> SBV a -> SBV a
(*!) :: (?loc :: CallStack) => SBV a -> SBV a -> SBV a
(/!) :: (?loc :: CallStack) => SBV a -> SBV a -> SBV a
negateChecked :: (?loc :: CallStack) => SBV a -> SBV a
infixl 6 +!, -!
infixl 7 *!, /!
instance CheckedArithmetic Word8 where
(+!) = checkOp2 ?loc "addition" (+) bvAddO
(-!) = checkOp2 ?loc "subtraction" (-) bvSubO
(*!) = checkOp2 ?loc "multiplication" (*) bvMulO
(/!) = checkOp2 ?loc "division" sDiv bvDivO
negateChecked = checkOp1 ?loc "unary negation" negate bvNegO
instance CheckedArithmetic Word16 where
(+!) = checkOp2 ?loc "addition" (+) bvAddO
(-!) = checkOp2 ?loc "subtraction" (-) bvSubO
(*!) = checkOp2 ?loc "multiplication" (*) bvMulO
(/!) = checkOp2 ?loc "division" sDiv bvDivO
negateChecked = checkOp1 ?loc "unary negation" negate bvNegO
instance CheckedArithmetic Word32 where
(+!) = checkOp2 ?loc "addition" (+) bvAddO
(-!) = checkOp2 ?loc "subtraction" (-) bvSubO
(*!) = checkOp2 ?loc "multiplication" (*) bvMulO
(/!) = checkOp2 ?loc "division" sDiv bvDivO
negateChecked = checkOp1 ?loc "unary negation" negate bvNegO
instance CheckedArithmetic Word64 where
(+!) = checkOp2 ?loc "addition" (+) bvAddO
(-!) = checkOp2 ?loc "subtraction" (-) bvSubO
(*!) = checkOp2 ?loc "multiplication" (*) bvMulO
(/!) = checkOp2 ?loc "division" sDiv bvDivO
negateChecked = checkOp1 ?loc "unary negation" negate bvNegO
instance CheckedArithmetic Int8 where
(+!) = checkOp2 ?loc "addition" (+) bvAddO
(-!) = checkOp2 ?loc "subtraction" (-) bvSubO
(*!) = checkOp2 ?loc "multiplication" (*) bvMulO
(/!) = checkOp2 ?loc "division" sDiv bvDivO
negateChecked = checkOp1 ?loc "unary negation" negate bvNegO
instance CheckedArithmetic Int16 where
(+!) = checkOp2 ?loc "addition" (+) bvAddO
(-!) = checkOp2 ?loc "subtraction" (-) bvSubO
(*!) = checkOp2 ?loc "multiplication" (*) bvMulO
(/!) = checkOp2 ?loc "division" sDiv bvDivO
negateChecked = checkOp1 ?loc "unary negation" negate bvNegO
instance CheckedArithmetic Int32 where
(+!) = checkOp2 ?loc "addition" (+) bvAddO
(-!) = checkOp2 ?loc "subtraction" (-) bvSubO
(*!) = checkOp2 ?loc "multiplication" (*) bvMulO
(/!) = checkOp2 ?loc "division" sDiv bvDivO
negateChecked = checkOp1 ?loc "unary negation" negate bvNegO
instance CheckedArithmetic Int64 where
(+!) = checkOp2 ?loc "addition" (+) bvAddO
(-!) = checkOp2 ?loc "subtraction" (-) bvSubO
(*!) = checkOp2 ?loc "multiplication" (*) bvMulO
(/!) = checkOp2 ?loc "division" sDiv bvDivO
negateChecked = checkOp1 ?loc "unary negation" negate bvNegO
instance (KnownNat n, BVIsNonZero n) => CheckedArithmetic (WordN n) where
(+!) = checkOp2 ?loc "addition" (+) bvAddO
(-!) = checkOp2 ?loc "subtraction" (-) bvSubO
(*!) = checkOp2 ?loc "multiplication" (*) bvMulO
(/!) = checkOp2 ?loc "division" sDiv bvDivO
negateChecked = checkOp1 ?loc "unary negation" negate bvNegO
instance (KnownNat n, BVIsNonZero n) => CheckedArithmetic (IntN n) where
(+!) = checkOp2 ?loc "addition" (+) bvAddO
(-!) = checkOp2 ?loc "subtraction" (-) bvSubO
(*!) = checkOp2 ?loc "multiplication" (*) bvMulO
(/!) = checkOp2 ?loc "division" sDiv bvDivO
negateChecked = checkOp1 ?loc "unary negation" negate bvNegO
-- | Zero-extend to given bits
zx :: Int -> SVal -> SVal
zx n a
| n < sa = error $ "Data.SBV: Unexpected zero extension: from: " ++ show (intSizeOf a) ++ " to: " ++ show n
| True = p `svJoin` a
where sa = intSizeOf a
s = hasSign a
p = svInteger (KBounded s (n - sa)) 0
-- | Sign-extend to given bits. Note that we keep the signedness of the argument.
sx :: Int -> SVal -> SVal
sx n a
| n < sa = error $ "Data.SBV: Unexpected sign extension: from: " ++ show (intSizeOf a) ++ " to: " ++ show n
| True = p `svJoin` a
where sa = intSizeOf a
mk = svInteger $ KBounded (hasSign a) (n - sa)
p = svIte (pos a) (mk 0) (mk (-1))
-- | Get the sign-bit
signBit :: SVal -> SVal
signBit x = x `svTestBit` (intSizeOf x - 1)
-- | Is the sign-bit high?
neg :: SVal -> SVal
neg x = signBit x `svEqual` svTrue
-- | Is the sign-bit low?
pos :: SVal -> SVal
pos x = signBit x `svEqual` svFalse
-- | Do these have the same sign?
sameSign :: SVal -> SVal -> SVal
sameSign x y = (pos x `svAnd` pos y) `svOr` (neg x `svAnd` neg y)
-- | Do these have opposing signs?
diffSign :: SVal -> SVal -> SVal
diffSign x y = svNot (sameSign x y)
-- | Check all true
svAll :: [SVal] -> SVal
svAll = foldr svAnd svTrue
-- | Are all the bits between a b (inclusive) zero?
allZero :: Int -> Int -> SBV a -> SVal
allZero m n (SBV x)
| m >= sz || n < 0 || m < n
= error $ "Data.SBV.Tools.Overflow.allZero: Received unexpected parameters: " ++ show (m, n, sz)
| True
= svAll [svTestBit x i `svEqual` svFalse | i <- [m, m-1 .. n]]
where sz = intSizeOf x
-- | Are all the bits between a b (inclusive) one?
allOne :: Int -> Int -> SBV a -> SVal
allOne m n (SBV x)
| m >= sz || n < 0 || m < n
= error $ "Data.SBV.Tools.Overflow.allOne: Received unexpected parameters: " ++ show (m, n, sz)
| True
= svAll [svTestBit x i `svEqual` svTrue | i <- [m, m-1 .. n]]
where sz = intSizeOf x
-- | Unsigned addition. Can only overflow.
bvuaddo :: Int -> SVal -> SVal -> (SVal, SVal)
bvuaddo n x y = (underflow, overflow)
where underflow = svFalse
n' = n+1
overflow = neg $ zx n' x `svPlus` zx n' y
-- | Signed addition.
bvsaddo :: Int -> SVal -> SVal -> (SVal, SVal)
bvsaddo _n x y = (underflow, overflow)
where underflow = svAll [neg x, neg y, pos (x `svPlus` y)]
overflow = svAll [pos x, pos y, neg (x `svPlus` y)]
-- | Unsigned subtraction. Can only underflow.
bvusubo :: Int -> SVal -> SVal -> (SVal, SVal)
bvusubo _n x y = (underflow, overflow)
where underflow = y `svGreaterThan` x
overflow = svFalse
-- | Signed subtraction.
bvssubo :: Int -> SVal -> SVal -> (SVal, SVal)
bvssubo _n x y = (underflow, overflow)
where underflow = svAll [neg x, pos y, pos (x `svMinus` y)]
overflow = svAll [pos x, neg y, neg (x `svMinus` y)]
-- | Unsigned multiplication. Can only overflow.
bvumulo :: Int -> SVal -> SVal -> (SVal, SVal)
bvumulo 0 _ _ = (svFalse, svFalse)
bvumulo n x y = (underflow, overflow)
where underflow = svFalse
n1 = n+1
overflow1 = signBit $ zx n1 x `svTimes` zx n1 y
-- From Z3 sources:
--
-- expr_ref ovf(m()), v(m()), tmp(m());
-- ovf = m().mk_false();
-- v = m().mk_false();
-- for (unsigned i = 1; i < sz; ++i) {
-- mk_or(ovf, a_bits[sz-i], ovf);
-- mk_and(ovf, b_bits[i], tmp);
-- mk_or(tmp, v, v);
-- }
-- overflow2 = v;
--
overflow2 = go 1 svFalse svFalse
where go i ovf v
| i >= n = v
| True = go (i+1) ovf' v'
where ovf' = ovf `svOr` (x `svTestBit` (n-i))
tmp = ovf' `svAnd` (y `svTestBit` i)
v' = tmp `svOr` v
overflow = overflow1 `svOr` overflow2
-- | Signed multiplication.
bvsmulo :: Int -> SVal -> SVal -> (SVal, SVal)
bvsmulo 0 _ _ = (svFalse, svFalse)
bvsmulo n x y = (underflow, overflow)
where underflow = diffSign x y `svAnd` overflowPossible
overflow = sameSign x y `svAnd` overflowPossible
n1 = n+1
overflow1 = (xy1 `svTestBit` n) `svXOr` (xy1 `svTestBit` (n-1))
where xy1 = sx n1 x `svTimes` sx n1 y
-- From Z3 sources:
-- expr_ref v(m()), tmp(m()), a(m()), b(m()), a_acc(m()), sign(m());
-- a_acc = m().mk_false();
-- v = m().mk_false();
-- for (unsigned i = 1; i + 1 < sz; ++i) {
-- mk_xor(b_bits[sz-1], b_bits[i], b);
-- mk_xor(a_bits[sz-1], a_bits[sz-1-i], a);
-- mk_or(a, a_acc, a_acc);
-- mk_and(a_acc, b, tmp);
-- mk_or(tmp, v, v);
-- }
-- overflow2 = v;
overflow2 = go 1 svFalse svFalse
where sY = signBit y
sX = signBit x
go i v a_acc
| i + 1 >= n = v
| True = go (i+1) v' a_acc'
where b = sY `svXOr` (y `svTestBit` i)
a = sX `svXOr` (x `svTestBit` (n-1-i))
a_acc' = a `svOr` a_acc
tmp = a_acc' `svAnd` b
v' = tmp `svOr` v
overflowPossible = overflow1 `svOr` overflow2
-- | Is this a concrete value?
known :: SVal -> Bool
known (SVal _ (Left _)) = True
known _ = False
-- | Unsigned multiplication, fast version using z3 primitives.
bvumuloFast :: Int -> SVal -> SVal -> (SVal, SVal)
bvumuloFast n x y
| known x && known y -- Not particularly fast, but avoids shipping of to the solver
= bvumulo n x y
| True
= (underflow, overflow)
where underflow = fst $ bvumulo n x y -- No internal version for underflow exists (because it can't underflow)
overflow = svMkOverflow Overflow_UMul_OVFL x y
-- | Signed multiplication, fast version using z3 primitives.
bvsmuloFast :: Int -> SVal -> SVal -> (SVal, SVal)
bvsmuloFast n x y
| known x && known y -- Not particularly fast, but avoids shipping of to the solver
= bvsmulo n x y
| True
= (underflow, overflow)
where underflow = svMkOverflow Overflow_SMul_UDFL x y
overflow = svMkOverflow Overflow_SMul_OVFL x y
-- | Unsigned division. Neither underflows, nor overflows.
bvudivo :: Int -> SVal -> SVal -> (SVal, SVal)
bvudivo _ _ _ = (underflow, overflow)
where underflow = svFalse
overflow = svFalse
-- | Signed division. Can only overflow.
bvsdivo :: Int -> SVal -> SVal -> (SVal, SVal)
bvsdivo n x y = (underflow, overflow)
where underflow = svFalse
ones = svInteger (KBounded True n) (-1)
topSet = svInteger (KBounded True n) (2^(n-1))
overflow = svAll [x `svEqual` topSet, y `svEqual` ones]
-- | Unsigned negation. Neither underflows, nor overflows.
bvunego :: Int -> SVal -> (SVal, SVal)
bvunego _ _ = (underflow, overflow)
where underflow = svFalse
overflow = svFalse
-- | Signed negation. Can only overflow.
bvsnego :: Int -> SVal -> (SVal, SVal)
bvsnego n x = (underflow, overflow)
where underflow = svFalse
topSet = svInteger (KBounded True n) (2^(n-1))
overflow = x `svEqual` topSet
-- | Detecting underflow/overflow conditions for casting between bit-vectors. The first output is the result,
-- the second component itself is a pair with the first boolean indicating underflow and the second indicating overflow.
--
-- >>> sFromIntegralO (256 :: SInt16) :: (SWord8, (SBool, SBool))
-- (0 :: SWord8,(False,True))
-- >>> sFromIntegralO (-2 :: SInt16) :: (SWord8, (SBool, SBool))
-- (254 :: SWord8,(True,False))
-- >>> sFromIntegralO (2 :: SInt16) :: (SWord8, (SBool, SBool))
-- (2 :: SWord8,(False,False))
-- >>> prove $ \x -> sFromIntegralO (x::SInt32) .== (sFromIntegral x :: SInteger, (sFalse, sFalse))
-- Q.E.D.
--
-- As the last example shows, converting to `sInteger` never underflows or overflows for any value.
sFromIntegralO :: forall a b. (Integral a, HasKind a, Num a, SymVal a, HasKind b, Num b, SymVal b) => SBV a -> (SBV b, (SBool, SBool))
sFromIntegralO x = case (kindOf x, kindOf (Proxy @b)) of
(KBounded False n, KBounded False m) -> (res, u2u n m)
(KBounded False n, KBounded True m) -> (res, u2s n m)
(KBounded True n, KBounded False m) -> (res, s2u n m)
(KBounded True n, KBounded True m) -> (res, s2s n m)
(KUnbounded, KBounded s m) -> (res, checkBounds s m)
(KBounded{}, KUnbounded) -> (res, (sFalse, sFalse))
(KUnbounded, KUnbounded) -> (res, (sFalse, sFalse))
(kFrom, kTo) -> error $ "sFromIntegralO: Expected bounded-BV types, received: " ++ show (kFrom, kTo)
where res :: SBV b
res = sFromIntegral x
checkBounds :: Bool -> Int -> (SBool, SBool)
checkBounds signed sz = (ix .< literal lb, ix .> literal ub)
where ix :: SInteger
ix = sFromIntegral x
s :: Integer
s = fromIntegral sz
ub :: Integer
ub | signed = 2^(s - 1) - 1
| True = 2^s - 1
lb :: Integer
lb | signed = -ub-1
| True = 0
u2u :: Int -> Int -> (SBool, SBool)
u2u n m = (underflow, overflow)
where underflow = sFalse
overflow
| n <= m = sFalse
| True = SBV $ svNot $ allZero (n-1) m x
u2s :: Int -> Int -> (SBool, SBool)
u2s n m = (underflow, overflow)
where underflow = sFalse
overflow
| m > n = sFalse
| True = SBV $ svNot $ allZero (n-1) (m-1) x
s2u :: Int -> Int -> (SBool, SBool)
s2u n m = (underflow, overflow)
where underflow = SBV $ (unSBV x `svTestBit` (n-1)) `svEqual` svTrue
overflow
| m >= n - 1 = sFalse
| True = SBV $ svAll [(unSBV x `svTestBit` (n-1)) `svEqual` svFalse, svNot $ allZero (n-1) m x]
s2s :: Int -> Int -> (SBool, SBool)
s2s n m = (underflow, overflow)
where underflow
| m > n = sFalse
| True = SBV $ svAll [(unSBV x `svTestBit` (n-1)) `svEqual` svTrue, svNot $ allOne (n-1) (m-1) x]
overflow
| m > n = sFalse
| True = SBV $ svAll [(unSBV x `svTestBit` (n-1)) `svEqual` svFalse, svNot $ allZero (n-1) (m-1) x]
-- | Version of 'sFromIntegral' that has calls to 'Data.SBV.sAssert' for checking no overflow/underflow can happen. Use it with a 'Data.SBV.safe' call.
sFromIntegralChecked :: forall a b. (?loc :: CallStack, Integral a, HasKind a, HasKind b, Num a, SymVal a, HasKind b, Num b, SymVal b) => SBV a -> SBV b
sFromIntegralChecked x = sAssert (Just ?loc) (msg "underflows") (sNot u)
$ sAssert (Just ?loc) (msg "overflows") (sNot o)
r
where kFrom = show $ kindOf x
kTo = show $ kindOf (Proxy @b)
msg c = "Casting from " ++ kFrom ++ " to " ++ kTo ++ " " ++ c
(r, (u, o)) = sFromIntegralO x
-- Helpers
l2 :: (SVal -> SVal -> (SBool, SBool)) -> SBV a -> SBV a -> (SBool, SBool)
l2 f (SBV a) (SBV b) = f a b
l1 :: (SVal -> (SBool, SBool)) -> SBV a -> (SBool, SBool)
l1 f (SBV a) = f a
signPick2 :: (Int -> SVal -> SVal -> (SVal, SVal)) -> (Int -> SVal -> SVal -> (SVal, SVal)) -> (SVal -> SVal -> (SBool, SBool))
signPick2 fu fs a b
| hasSign a = let (u, o) = fs n a b in (SBV u, SBV o)
| True = let (u, o) = fu n a b in (SBV u, SBV o)
where n = intSizeOf a
signPick1 :: (Int -> SVal -> (SVal, SVal)) -> (Int -> SVal -> (SVal, SVal)) -> (SVal -> (SBool, SBool))
signPick1 fu fs a
| hasSign a = let (u, o) = fs n a in (SBV u, SBV o)
| True = let (u, o) = fu n a in (SBV u, SBV o)
where n = intSizeOf a
checkOp1 :: (HasKind a, HasKind b) => CallStack -> String -> (a -> SBV b) -> (a -> (SBool, SBool)) -> a -> SBV b
checkOp1 loc w op cop a = sAssert (Just loc) (msg "underflows") (sNot u)
$ sAssert (Just loc) (msg "overflows") (sNot o)
$ op a
where k = show $ kindOf a
msg c = k ++ " " ++ w ++ " " ++ c
(u, o) = cop a
checkOp2 :: (HasKind a, HasKind c) => CallStack -> String -> (a -> b -> SBV c) -> (a -> b -> (SBool, SBool)) -> a -> b -> SBV c
checkOp2 loc w op cop a b = sAssert (Just loc) (msg "underflows") (sNot u)
$ sAssert (Just loc) (msg "overflows") (sNot o)
$ a `op` b
where k = show $ kindOf a
msg c = k ++ " " ++ w ++ " " ++ c
(u, o) = a `cop` b